Method for lining curves



p 1967 A. WARNICK 3,343,496

METHOD FOR LINING CURVES 7 Filed March 31. 1965 2 Sheets-Sheet 1 INVENTOR.

A L WA'M/ICI/ BY *zsarr 2 Sheets-Sheet 2 Filed March 31, 1965 INVENIOR. wow kR CK United States Patent i 3,343,496 METHOD FOR LINING CURVES Adolf War-nick, Nurnbnrg, Germany, assignor to Franz Plasser Bahnbaumaschinen, Vienna, Austria Filed Mar. 31, 1965, Ser. No. 444,354 Claims priority, application Germany, Apr. 3, 1964, W 36,494; Apr. 17, 1964, W 36,597; Austria, Feb. 10, 1965, A 1,164/65 7 Ciaims. (Cl. 1047) The present invention relates to the lining of railroad track curves to produce a track curve section constituting a substantially circular arc extending between two end points connected by a physical or imaginary chord. In such curve lining, a first portion of the track curve section extends between a first one of the end points and a first intermediate point, this forming a first and lined portion of the circular arc. Successive intermediate points in a second portion of the track curve section extending between the first intermediate point and a second one of the end points are lined as the chord is advanced along the track, with one of its ends always in one lined track point and another lined track point adjacent to the lined end point above the chord.

It is a primary object of this invention to simplify curve lining so that it may be efiectuated manually as well as by mobile track liners.

It is a more specific object of the invention to line curves on the basis of a single chord and to make use of well known and simple geometrical theorems concerning the circle in determining the correct ordinate of a second intermediate track curve section point in relation to the single chord to line this second track point.

These and other objects and advantages are accomplished in accordance with the present invention by establishing the length of a first straight line from the chord to the first, previously lined intermediate point of a first portion of the track curve section and establishing a second straight line from the chord to the second intermediate point to be lined. The second straight line is geometrically analogous to the first straight line and its correct length is, therefore, derivable from the length of the first straight line on the basis of geometrical theorems concerning the circle, if the track curve section is to form a circular arc. T0 line the second intermediate point, the second track curve section portion extending between the first intermediate point and the second end point is moved perpendicularly to the direction of elongation of the track until the second straight line has the derived length from the chord to the second intermediate point.

In one embodiment of this invention, the two straight lines are the ordinates of the first and second intermediate points, respectively. If desired, the distances of the ordinates from the respective end points may be the same, in which case they are of the same length after the second intermediate track curve section point has been lined, requiring no calculation.

In another embodiment of the invention, two intersecting secants are laid through respective ones of the end points of the track curve section, with the points of intersection lying within or outside the circular arc. In one variation of this embodiment, the first secant extends from the first end point to the second intermediate point and the second secant extends from the second end point to the first and lined intermediate point, with the point of intersection of the secants lying within the circular arc. In another variation, the first secant extends from the first end point through the first intermediate point and the second secant extends from the second end point through the second intermediate point, with the point of intersection of the secants outside the circular arc.

3,343,496 Patented Sept. 26, 1967 Various arrangements for carrying out these methods of the invention may be provided, all of them providing two intersecting means defining the indicated straight lines, such as rigid rods or tautly drawn, flexible elongated members, such as ropes. Conventional mobile track lining equipment including means for laterally moving tracks may be used for the purposes of the invention and, not forming a novel part of the invention, will not be described or illustrated.

The above and other objects, advantages and features of the present invention will become more apparent in the following detailed description of certain preferred embodiments thereof, taken in conjunction with the accompanying drawing wherein FIGS. 1 to 6 schematically illustrate difierent modifications of lining methods and apparatus according to this invention.

In the drawing, like reference numerals indicate like features in all figures.

Referring first to FIG. 1, there is shown a railroad track curve section G forming a circular arc of the length d. A chord 5 extends between the end points 1 and 4 of the track curve section G. A first track curve section portion a extending from end point 1 to point 2 has previously been lined while point 3 of the track curve section is to be lined in accordance with this invention to line the second portion b+c of the track curve section ex tending from previously aligned point 2 to point 4.

According to the invention, the correct location of track point 3 is obtained by measuring the ordinate k of aligned point 2 in respect of chord 5, and moving the track at point 3 until its ordinate k in respect of chord 5 has the geometrically corresponding parameter. The corresponding parameter may be readily calculated on the basis of relationships in the known geometry of circles.

In the particular embodiment shown in FIG. 1, the ordinate of the lined point or station 2 has the same distance from the initial point or station 1 of the track curve section G as the ordinate of the point or station 3 to be lined has from the end point or station 4. Thus, stations 2 and 3 are symmetrically positioned in the curve section and the lengths of ordinates I2 and in, are, therefore, the same. This saves the step of calculating the length of ordinate 11 on the basis of that of ordinate h In this specific case, where a=c, the error is reduced by b/d. If b=3.0 meters and d=30.0 meters, the reduction is one tenth.

In the embodiment of FIG. 2, stations 2 and 3 are not symetrically located on the track curve section G. As in the embodiment of FIG. 1, theordinate I2 of aligned station 2 is measured in respect of chord 5 and the geometrically corresponding length of ordinate h of station 3 on the circular arc G is determined by means of a well known geometric theorem. For this purpose, a simple arrangement may be provided to consist of two means each defining a straight line, such as rods x and y, interconnected intermediate their ends by a pivot 6. The pivot 6 lies between chord 5 and the track curve G and the two rods are so positioned that rod x passes through aligned end station 1 of the track curve while rod y passes through aligned intermediate station 2 and the other end station 4 of the track curve section G. In this manner, the two rods form secants of the circular arc and, according to the well known theorem of secants, the products of the secant sections 2.1 and gi of the two intersecting secants x and y must be equal for a circular arc. Thus, since the lengths of secant sections g, i and 2 may be readily measured and the product g.i is thus known, the length of 7 may be readily calculated, e being known and the product e.f being equal to g.i. The length of 1 determines the location of station 3, of course, and the track is moved until its point 3 defines the length calculated for 1.

After station 3 of the track curve has thus been aligned, the apparatus is advanced until station 2 becomes end station 1 and aligned station 3 becomes station 2, and the aligning procedure is repeated.

The embodiment of FIG. 3 differs from that of FIG. 2 primarily in that the secants intersect in a pivot 6' outside the circular arc G. In this case, afirst rod of the length k is laid through lined track points 1 and 2. A :second rod of the length n extends from the interconmecting pivot 6' of the two rods through track section end point 4. If the two intersecting rods are to form secants of a circular are over chord 5, the product of the length k of the one secant and the distance I from the point of intersection 6 .to the point of the are 2 must be equal to the product of the length n of the other secant and the distance m from the point of intersection 6 to the point of the arc '3 on the other secant. The distance In is calculated in the manner indicated in connection with the similar embodiment of FIG. 2 and point 3 of the track curve section is then moved accordingly until the distance from pivot 6 to the track has the calculated .value.

The distance I is readilycalculated to a. desired degree of accuracy by the following equations derived from the geometry of triangles:

Since, as explained hereinabove, k.l=n.m, the ratio of k:n=m:l. The track must be moved at station 3 until this ratio isreached.

The schematically illustrated procedure of FIG. 3 is illustrated in connection with three specific structural ernbodiments in FIGS. 4 to 6.

In FIG. 4, station 3 of the track curve section G is to be lined so that the curve section becomes a circular arc. For this purpose, the point of intersection 6' of the two means ;7 and 8 defining two straight intersecting lines is mounted transversely movable in relation to the track. For instance, the two straight line defining means may be tautly drawn ropes each having one of their ends attached to a pivot pin mounted on a bearing threadedly supported on a spindle 13 extending transversely of the track. In this manner, the pivot pin 6' may be moved transversely in relation to the track rails upon rotation of -the spindle. As illustrated, stations 1, 2, 3 and 4 of the track curve section are constituted by simple trucks mounted on the track rails and the straight lines -or secants 7 and 8 extend through the midpoints of the trucks. Ac.- tually, the points of intersection, i.e. points '1, 2, '3 and 4 of the circular arc may be chosen at any constant spacing from the track rails as long as the spacing of all points is the same.

Points 1 and 2 forming part of the lined track curve section, rope or rod 7 is attached at one end to the aligned end station 1 and with its other end to pivot pin 6'. The latter is then transversely moved until a straight line extends between points 1, 2 and 6. The other rope or rod 8 has its two ends attached, respectively, to point 6' and the other end point 4 of the track curve section. After point 6' has been moved in the indicated manner, track point 3 needs to be moved for lining until it comes to hem the straight line 8.

In the modification of FIG. 5, the identical principles are followed in using two rods 9 and 10 pivotally interconnected at point 6'. Rod 9 extends through lined track points 1 and 2 while rod 10 passes from pivot 6 through track point 3 to be lined. Another rod is connected between track point 3 and track curve section end point 4 and point 3 is transversely moved until the indicated angle between rods 10 and 11 is zero, i.e. until the two rods form a straight line.

In 1 fu ther modification of FIG. 6, substantially the same principles are used by interconnecting points 1, 2 and 6' by a rigid rod 9 and extending a straight rod or rope 8 from pivot 6' to track curve section end point 4. Track point 3 is then moved perpendicularly to the direction of elongation of the track until it comes to lie on the straight line defined by means 8.

In all of these variations of the procedure illustrated geometrically in FIG. 3, it is essential that the points through which the straight lines or secants pass have the same distance from a respective one of the track rails and they will advantageously be chosen at the midpoints of the track.

Since the track is moved transversely of its elongation at station 3, it is advantageous to mount there indicating means showing .an operator of .a track moving apparatus to what side and to what extent to move the track laterally. Such an indicator is schematically shown at .12 and readily enables the operator to determine when track point 3 has reached its lined position.

On the indicator 12, the ordinates of the lined point 2 and point 3 to be lined are preferably indicated on such a scale by two indicating hands that the two hands are in line when point 3 has been moved into the desired posiiton.

While the present invention has been specifically described and illustratedin connection with certain .preferred embodiments, it will be clearly understood that many modifications and variations may occur to those skilled in this art without departing from the spirit and scope of this invention as defined in the appended claims. More particularly, it will be obvious that mobile automated track lining equipment may be used wherein track sections are laterally moved while the equipment moves continuously forwardly on the track, the track moving parameters derived according to the invention being automatically transmitted to the equipment and such parameters being used to control the lateral track movement.

What is claimed is:

1. A method of lining a track curve to produce a track curve section constituting .a substantially circular are extending between two end points, a chord extending between said end points and a first portion of the track curve section extending between a first one of said end points and a first intermediate point of the track curve section having been lined to form a first portion of said circular arc, the steps of establishing the length of a first straight line from the chord tothe first intermediate point, establishing ,a second straight line from the chord to a second intermediate point in a second portion of the track curve section extending between the first intermediate point and the second end point, the second straightline being geometrically analogous to the first straight line and its length being accordingly derivable from the length of the first straight line on the basis of geometrical theorems concerning the circle, and moving the second track curve section portion perpendicularly to the direction of elongation of the track until the second straight line has the derived length from the chord to the second intermeditae point.

2. The method of claim 1, wherein the first and second straight lines are the ordinates of the first and second intermediate points, respectively.

3. The method of claim 2, wherein the distance of the ordinate of the first intermediate point from the first end point is the same as the distance of the ordinate of the second intermediate point from the second end point, whereby the ordinates of said intermediate points are of the same length.

:4. A method of lining a track curve to produce a'track curve section constituting a substantially circular are extending between two end points, including the steps of establishing a chord between said end points, a first portion of the track curve section extending between a first one of said end points and a first intermediate point of the track curve section having been lined to form a first portion of the circular arc, establishing an ordinate from the chord to the first intermediate point, establishing a second ordinate from the chord to a second intermediate point in a second portion of the track curve section extending between the first intermediate point and the second end point, the length of the second ordinate being derivable from the length of the first-named ordinate on the basis of geometrical theorems concerning the circle, and moving the second track curve section portion perpendicularly to the direction of elongation of the track until the second ordinate has the derived length from the chord to the second intermediate point.

5. A method of lining a track curve to produce a track curve section constituting a substantially circular are extending between two end points, a first portion of the track curve section extending between a first one of said end points and a first intermediate point of the track curve section having been lined to form a first portion of said circular arc, and a second portion of the track curve section extending between the first intermediate point and the second end point of the track curve section, a second intermediate point in said second portion to be lined, the steps of laying two intersecting secants through respective ones of said end points and intermediate points, the length of the secant through the lined intermediate point being determined and the length of the secant through the second intermediate point being derivable from said determined length on the basis of geometric theorems concerning the secants of a circular arc, and moving the second track curve section portion perpendicularly to the direction of elongation of the track until the secant through the second intermediate point has the derived length to the second intermediate point.

6. The method of claim 5, wherein a first one of said secants extends from the first end point to a second intermediate point, a second one of the secant extends from the second end point to the first and lined intermediate point, and the point of intersection of the secants is within the circular arc.

7. The method of claim 5, wherein a first one of said secants extends from the first end point through the first and lined intermediate point, a second one of the secants extends from the second end point to the second intermediate point to be lined, and the point of intersection of the secants is outside the circular arc.

No references cited.

ARTHUR L. LA POINT, Primary Examiner.

R. A. BERTSCH, Assistant Examiner. 

1. A METHOD OF LINING A TRACK CURVE TO PRODUCE A TRACK CURVE SECTION CONSTITUTING A SUBSTANTIALLY CIRCULAR ARC EXTENDING BETWEEN TWO END POINTS, A CHORD EXTENDING BETWEEN SAID END POINTS AND A FIRST PORTION OF THE TRACK CURVE SECTION EXTENDING BETWEEN A FIRST ONE OF SAID END POINTS AND A FIRST INTERMEDIATE POINT OF THE TRACK CURVE SECTION HAVING BEEN LINED TO FORM A FIRST PORTION OF SAID CIRCULAR ARC, THE STEPS OF ESTABLISHING THE LENGTH OF A FIRST STRAIGHT LINE FROM THE CHORD TO THE FIRST INTERMEDIATE POINT, ESTABLISHING A SECOND STRAIGHT LINE FROM THE CHORD TO A SECOND INTERMEDIATE POINT IN A SECOND PORTION OF THE TRACK CURVE SECTION EXTENDING BETWEEN THE FIRST INTERMEDIATE POINT AND THE SECOND END POINT, THE SECOND STRAIGHT LINE BEING GEOMETRICALLY ANALOGOUS TO THE FIRST STRAIGHT LINE AND ITS LENGTH BEING ACCORDINGLY DERIVABLE FROM THE LENGTH OF THE FIRST STRAIGHT LINE ON THE BASIS OF GEOMETRICAL THEOREMS CONCERNING THE CIRCLE, AND MOVING THE SECOND TRACK CURVE SECTION PORTION PERPENDICULARLY TO THE DIRECTION OF ELONGATION OF THE TRACK UNTIL THE SECOND STRAIGHT LINE HAS THE DERIVED LENGTH FROM THE CHORD TO THE SECOND INTERMEDIATE POINT. 